Problem: Multiply the following complex numbers: $({3-4i}) \cdot ({-1+3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3-4i}) \cdot ({-1+3i}) = $ $ ({3} \cdot {-1}) + ({3} \cdot {3}i) + ({-4}i \cdot {-1}) + ({-4}i \cdot {3}i) $ Then simplify the terms: $ (-3) + (9i) + (4i) + (-12 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (9 + 4)i - 12i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (9 + 4)i - (-12) $ The result is simplified: $ (-3 + 12) + (13i) = 9+13i $